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# Science Fair Project Encyclopedia

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# Semiperfect number

In mathematics, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors.

The first few semiperfect numbers are 6, 12, 18, 20, 24, 28, 30, 36, 40, ... ; every multiple of a semiperfect number is semiperfect, and every number of the form 2mp for a natural number m and a prime number p such that 2m < p < 2m + 1 is also semiperfect.

A semiperfect number that is equal to the sum of all its proper divisors is called a perfect number; an abundant number which is not semiperfect is called a weird number.